相关论文: A non-equilibrium equality in Hamiltonian chaos
We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the…
Extended nonequilibrium systems can be studied in the framework of field theory or from dynamical systems perspective. Here we report numerical evidence that the sum of a well-defined number of instantaneous Lyapunov exponents for the…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto…
The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…
Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…
Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply…
Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In…
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of…
This paper is concerned with a linear-quadratic non-zero sum differential game with asymmetric delayed information. To be specific, two players exist time delays simultaneously which are different, leading the dynamical system being an…
A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any…
Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free energy landscapes under persistent currents. Within the framework of…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…
For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which…